U.S. patent application number 09/932006 was filed with the patent office on 2002-03-07 for optical element and manufacturing method thereof.
This patent application is currently assigned to DAI NIPPON PRINTING CO., LTD.. Invention is credited to Hamano, Tomohisa, Kitamura, Mitsuru.
Application Number | 20020027702 09/932006 |
Document ID | / |
Family ID | 18752371 |
Filed Date | 2002-03-07 |
United States Patent
Application |
20020027702 |
Kind Code |
A1 |
Kitamura, Mitsuru ; et
al. |
March 7, 2002 |
Optical element and manufacturing method thereof
Abstract
A hologram that can obtain high diffraction efficiency when
reconstructed and is superior in productivity is provided. An
arbitrary object image and a recording surface in which
representative points are disposed with predetermined pitches are
defined by use of a computer. At the position of each individual
representative point, a complex amplitude for the wave front of
object light emitted from the object image is calculated, and a
complex amplitude distribution is calculated on the recording
surface. This complex amplitude distribution is expressed by a
three-dimensional cell having a groove in the surface thereof. Four
kinds of groove depths are defined in accordance with the phase
.theta., and seven kinds of groove widths are defined in accordance
with the amplitude A. Thereby, 28 kinds of three-dimensional cells
in total are prepared, and a three-dimensional cell corresponding
to the phase .theta. and amplitude A of the complex amplitude for
the representative point is disposed at the position of each
representative point. One of the 28 kinds of three-dimensional
cells is disposed at the position of each representative point on
the recording surface, and thereby a hologram-recording medium is
formed as a set of three-dimensional cells. A reconstructed image
is obtained by the phase/amplitude modulating function of the
groove part of each cell.
Inventors: |
Kitamura, Mitsuru; (Tokyo,
JP) ; Hamano, Tomohisa; (Tokyo, JP) |
Correspondence
Address: |
Ladas & Parry
26 West 61st. Street
New York
NY
10023
US
|
Assignee: |
DAI NIPPON PRINTING CO.,
LTD.
|
Family ID: |
18752371 |
Appl. No.: |
09/932006 |
Filed: |
August 17, 2001 |
Current U.S.
Class: |
359/276 ;
359/279 |
Current CPC
Class: |
G03H 2240/50 20130101;
G03H 2240/13 20130101; G03H 2224/04 20130101; G03H 2001/226
20130101; G03H 2210/40 20130101; G03H 1/0808 20130101; G03H
2001/0858 20130101; G03H 1/0841 20130101; G03H 1/028 20130101; G03H
1/0891 20130101; G03H 2001/2223 20130101 |
Class at
Publication: |
359/276 ;
359/279 |
International
Class: |
G02F 001/01 |
Foreign Application Data
Date |
Code |
Application Number |
Sep 1, 2000 |
JP |
2000-265042 |
Claims
What is claimed is:
1. An optical element consisting of a set of a plurality of
three-dimensional cells, wherein: a specific amplitude and a
specific phase are defined in each individual cell, and said
individual cell has a specific optical property so that, when
incident light is provided to the cell, emission light is obtained
by changing an amplitude and a phase of the incident light in
accordance with the specific amplitude and the specific phase
defined in the cell.
2. The optical element as set forth in claim 1, wherein each cell
has an amplitude-modulating part provided with transmittance
corresponding to a specific amplitude.
3. The optical element as set forth in claim 1, wherein each cell
has an amplitude-modulating part provided with reflectivity
corresponding to a specific amplitude.
4. The optical element as set forth in claim 1, wherein each cell
has an amplitude-modulating part provided with an effective area
corresponding to a specific amplitude.
5. The optical element as set forth in claim 1, wherein each cell
has a phase-modulating part provided with a refractive index
corresponding to a specific phase.
6. The optical element as set forth in claim 1, wherein each cell
has a phase-modulating part provided with an optical path length
corresponding to a specific phase.
7. The optical element as set forth in claim 1, wherein each cell
has a concave part formed by hollowing a part provided with an area
corresponding to a specific amplitude by a depth corresponding to a
specific phase.
8. The optical element as set forth in claim 7, wherein a surface
where the concave part of each cell is formed serves as a
reflecting surface, and incident light provided to the cell is
reflected by the reflecting surface and thereby turns into emission
light.
9. The optical element as set forth in claim 7, wherein each cell
includes a main body layer having a concave part and a protective
layer with which a surface where the concave part of the main body
layer is formed is covered, and the ma in body layer and the
protective layer are made of materials different from each
other.
10. The optical element as set forth in claim 9, wherein the main
body layer and the protective layer are made of transparent
materials different in a refractive index from each other, and
incident light provided to the cell passes through the main body
layer and the protective layer and thereby turns into emission
light.
11. The optical element as set forth in claim 9, wherein a boundary
between the main body layer and the protective layer forms a
reflecting surface, and incident light provided to the cell is
reflected by the reflecting surface and thereby turns into emission
light.
12. The optical element as set forth in claim 1, wherein each cell
has a convex part formed by protruding a part provided with an area
corresponding to a specific amplitude by a height corresponding to
a specific phase.
13. The optical element as set forth in claim 12, wherein a surface
where the convex part of each cell is formed serves as a reflecting
surface, and incident light provided to the cell is reflected by
the reflecting surface and thereby turns into emission light.
14. The optical element as set forth in claim 12, wherein each cell
includes a main body layer a convex part and a protective layer
with which a surface where the convex part of the main body layer
is formed is covered, and the main body layer and the protective
layer are made of materials different from each other.
15. The optical element as set forth in claim 14, wherein the main
body layer and the protective layer are made of transparent
materials different in a refractive index from each other, and
incident light provided to the cell passes through the main body
layer and the protective layer and thereby turns into emission
light.
16. The optical element as set forth in claim 14, wherein a
boundary between the main body layer and the protective layer forms
a reflecting surface, and incident light provided to the cell is
reflected by the reflecting surface and thereby turns into emission
light.
17. The optical element as set forth in claim 1, wherein each cell
is arranged one-dimensionally.
18. The optical element as set forth in claim 1, wherein each cell
is arranged two-dimensionally.
19. The optical element as set forth in claim 18, wherein a
longitudinal pitch of each cell and a lateral pitch of each cell
are arranged so as to be an equal pitch.
20. The optical element as set forth in claim 1, wherein a complex
amplitude distribution of object light from an object image is
recorded so that the object image is reconstructed when observed
from a predetermined viewing point so as to be usable as a
hologram.
21. A method for manufacturing an optical element where a
predetermined object image is recorded, the method comprising: a
cell defining step of defining a set of a plurality of
three-dimensional virtual cells; a representative-point defining
step of defining a representative point for each virtual cell; an
object image defining step of defining an object image to be
recorded; an amplitude phase defining step of defining a specific
amplitude and a specific phase in each virtual cell by calculating
a complex amplitude at a position of each representative point of
object light emitted from the object image; and a physical cell
forming step of replacing each virtual cell with a real physical
cell and forming an optical element that consists of a set of
three-dimensional physical cells; wherein, at the physical cell
forming step, when predetermined incident light is given to each
physical cell, replacement is carried out by each physical cell
having a specific optical property so as to obtain emission light
that has changed an amplitude and a phase of the incident light in
accordance with a specific amplitude and a specific phase defined
in the virtual cell corresponding to the physical cell.
22. The manufacturing method for the optical element as set forth
in claim 21, wherein, at the cell defining step, a cell set is
defined by arranging block-like virtual cells
one-dimensionally.
23. The manufacturing method for the optical element as set forth
in claim 21, wherein, at the cell defining step, a cell set is
defined by arranging block-like virtual cells
two-dimensionally.
24. The manufacturing method for the optical element as set forth
in claim 21, wherein, at the amplitude phase defining step, a
plurality of point light sources are defined on the object image,
and object light of a spherical wave having a predetermined
amplitude and a predetermined phase is regarded as being emitted
from each point light source, and a totaled complex amplitude of
the object light from the point light sources at a position of each
representative point is calculated at a predetermined standard
time.
25. The manufacturing method for the optical element as set forth
in claim 24, wherein K point light sources that emit object light
whose wavelength is .lambda. are defined on the object image, and
if an amplitude of object light emitted from a k-th point light
source O(k) (k=1 to K) is represented as Ak, and a phase thereof is
represented as .theta. k, and a distance between a predetermined
representative point P and the k-th point light source O(k) is
represented as rk, a totaled complex amplitude of the object light
from the K point light sources at the predetermined representative
point P is calculated as follows: .SIGMA..sub.(k=1,K)(Ak/r-
k.multidot.cos (.theta.k+2 .pi.rk/.lambda.) +iAk/rk.multidot.sin
(.theta.k.+-.2 .pi.rk/.lambda.)).
26. The manufacturing method for the optical element as set forth
in claim 21, wherein, at the physical cell forming step, each
virtual cell is replaced with a physical cell having a concave part
formed by hollowing a part provided with an area corresponding to a
specific amplitude by a depth corresponding to a specific
phase.
27. The manufacturing method for the optical element as set forth
in claim 26, wherein: a refractive index of a material filled in
the concave part of the physical cell is represented as n1, a
refractive index of another material in contact with the material
n1 is represented as n2, a wavelength of object light is
represented as .lambda., a maximum depth dmax of the concave part
is set to be dmax=.lambda./.vertline.n1-n2.vertl- ine., a depth d
corresponding to a specific phase .theta. is determined by the
expression d=.lambda..multidot..theta./2(n1-n2).pi. when n1>n2,
and is determined by the expression d=dmax
-.lambda..multidot..theta./2(n- 2-n1).pi. when n1<n2, and an
object image is reconstructed by transmission light that has passed
through the concave part.
28. The manufacturing method for the optical element as set forth
in claim 26, wherein: a refractive index of a material filled in
the concave part of the physical cell is represented as n, a
wavelength of object light is represented as .lambda., a maximum
depth of the concave part is set to be dmax =.lambda./2n, a depth d
corresponding to the specific phase .theta. is determined by the
expression d=.lambda..multidot..theta./4n.pi., and an object image
is reconstructed by reflected light that has been reflected by the
boundary of the concave part.
29. The manufacturing method for the optical element as set forth
in claim 26, wherein .alpha. kinds of a plurality of areas are
defined as areas corresponding to a specific amplitude, .beta.
kinds of a plurality of depths are defined as depths corresponding
to a specific phase so as to prepare .alpha..times..beta. kinds of
physical cells in total, and each virtual cell is replaced with a
physical cell closest in a necessary optical property among said
physical cells.
30. The manufacturing method for the optical element as set forth
in claim 21, wherein, at the physical cell forming step, each
virtual cell is replaced with a physical cell having a convex part
formed by protruding a part provided with an area corresponding to
a specific amplitude by a height corresponding to a specific
phase.
31. The manufacturing method for the optical element as set forth
in claim 30, wherein: a refractive index of a material that
constitutes the convex part is represented as n1, a refractive
index of another material in contact with the material n1 is
represented as n2, a wavelength of object light is represented as
.lambda., a maximum height dmax of the convex part is set to be
dmax=.lambda./.vertline.n1-n2.vertline., a height d corresponding
to a specific phase .theta. is determined by the expression
d=.lambda..multidot..theta./2(n1-n2).pi. when n1>n2, and is
determined by the expression d=dmax
-.lambda..multidot..theta./2(n2-n1).pi. when n1<n2, and an
object image is reconstructed by transmission light that has passed
through the convex part.
32. The manufacturing method for the optical element as set forth
in claim 30, wherein: a refractive index of a material that
constitutes the convex part is represented as n, a wavelength of
object light is represented as .lambda., a maximum height dmax of
the convex part is set to be dmax=.lambda./2n, a height d
corresponding to the specific phase .theta. is determined by the
expression d=.lambda..multidot..theta./4n.pi., and an object image
is reconstructed by reflected light that has been reflected by the
boundary of the convex part.
33. The manufacturing method for the optical element as set forth
in claim 30, wherein .alpha. kinds of a plurality of areas are
defined as areas corresponding to a specific amplitude, .beta.
kinds of a plurality of heights are defined as heights
corresponding to a specific phase so as to prepare
.alpha..times..beta. kinds of physical cells in total, and each
virtual cell is replaced with a physical cell closest in a
necessary optical property among said physical cells.
34. The manufacturing method for the optical element as set forth
in claim 21, further comprising a phase-correcting step of
correcting the specific phase defined for each virtual cell in
consideration of a direction of illumination light projected when
reconstructed.
35. The manufacturing method for the optical element as set forth
in claim 21, further comprising a phase-correcting step of
correcting the specific phase defined for each virtual cell in
consideration of a position of a viewing point when
reconstructed.
36. The manufacturing method for the optical element as set forth
in claim 21, wherein: at the cell defining step, a cell set of
virtual cells arranged on a two-dimensional matrix is defined by
arranging the virtual cells horizontally and vertically, at the
amplitude phase defining step, a plurality of M point light source
rows that are each extended in a horizontal direction and are
mutually disposed in a vertical direction are defined on an object
image, and M groups in total are defined by defining virtual cells
that belong to a plurality of rows contiguous in the vertical
direction in the two-dimensional matrix as one group, the M point
light source rows and the M groups are caused to correspond to each
other in accordance with an arrangement order relative to the
vertical direction, and a totaled complex amplitude at a position
of each representative point is calculated on a supposition that
object light emitted from a point light source in an m-th point
light source row (m=1 to M) reaches only virtual cells that belongs
to an m-th group.
Description
BACKGROUND OF THE INVENTION
[0001] The present invention relates to an optical element and a
manufacturing method thereof and, more particularly, relates to an
optical element capable of recording a stereoscopic image as a
hologram and reconstructing the image, and a manufacturing method
thereof.
[0002] A holographic technique is conventionally known as a method
for recording a stereoscopic image on a medium and reconstructing
this image. A hologram produced by this method is used in various
fields, such as ornamental art or anti-counterfeit seals. In order
to optically produce the hologram, it is common to record the
interference fringe between object light reflected from an object
and reference light on a photosensitive medium. A laser beam
superior in coherence is usually used as a light source for the
object light and the reference light. Generally, the motion of
electromagnetic radiation, such as light, can be regarded as the
propagation of a wave front provided with amplitude and a phase,
and it can be said that the hologram is an optical element that
functions to reconstruct such a wave front. Therefore, it is
necessary to record information for accurately reconstructing the
amplitude and phase of the object light at each position in space
on the recording medium of the hologram. If interference fringes
generated by the object light and the reference light are recorded
on the photosensitive medium, information that includes both the
phase and the amplitude of the object light can be recorded, and,
by projecting illumination reconstructing light equivalent to the
reference light onto the medium, a part of the illumination
reconstructing light can be observed as light provided with a wave
front equivalent to the object light.
[0003] If the hologram is produced by an optical method using a
laser beam or the like in this way, the phase and amplitude of the
object light can be recorded only as interference fringes resulting
from interference between the object light and the reference light.
The reason is that the photosensitive medium has a property of
being photosensitized in accordance with light intensity. On the
other hand, a technique of producing a hologram by computations
with use of a computer has recently been put to practical use. This
technique is called a "CGH" (Computer-Generated Hologram) method,
in which the wave front of object light is calculated by use of a
computer, and its phase and its amplitude are recorded on a
physical medium according to a certain method so as to produce a
hologram. The employment of this computational holography, of
course, enables the recording of an image as interference fringes
between object light and reference light, and, in addition, enables
the recording of information for the phase and amplitude of the
object light directly onto a recording surface without using the
reference light. For example, a recording method has been proposed
in which an amplitude is represented by the size of an opening
formed in a recording medium whereas a phase is represented by the
position of the opening or in which a medium is made up of two
recording layers on one of which an amplitude is recorded and on
the other one of which a phase is recorded.
[0004] The method for recording an image as interference fringes
that has been widely used as an optical hologram producing method
is at an advantage in that productivity is high because, in
general, a reconstructed image with high resolution can be obtained
and because an optical method is used, but it is at a disadvantage
in that an image darkens because diffraction efficiency by
interference fringes is poor when reconstructed. By contrast, the
method for recording the phase and amplitude of object light
directly onto a medium that has been proposed as one of the
computer-generated hologram methods is at an advantage in that high
diffraction efficiency can be obtained, but it is at a disadvantage
in that, practically, productivity decreases because the recording
of the phase and the amplitude onto the medium is technically
difficult.
SUMMARY OF THE INVENTION
[0005] It is therefore an object of the present invention to
provide an optical element that can obtain high diffraction
efficiency when reconstructed and that is excellent in
productivity.
[0006] (1) The first feature of the present invention resides in an
optical element consisting of a set of a plurality of
three-dimensional cells, wherein:
[0007] a specific amplitude and a specific phase are defined in
each individual cell,
[0008] and the individual cell has a specific optical property so
that, when incident light is provided to the cell, emission light
is obtained by changing an amplitude and a phase of the incident
light in accordance with the specific amplitude and the specific
phase defined in the cell.
[0009] (2) The second feature of the present invention resides in
the optical element according to the first feature, wherein each
cell has an amplitude-modulating part provided with transmittance
corresponding to a specific amplitude.
[0010] (3) The third feature of the present invention resides in
the optical element according to the first feature, wherein each
cell has an amplitude-modulating part provided with reflectivity
corresponding to a specific amplitude.
[0011] (4) The fourth feature of the present invention resides in
the optical element according to the first feature, wherein each
cell has an amplitude-modulating part provided with an effective
area corresponding to a specific amplitude.
[0012] (5) The fifth feature of the present invention resides in
the optical element according to the first to the fourth features,
wherein each cell has a phase-modulating part provided with a
refractive index corresponding to a specific phase.
[0013] (6) The sixth feature of the present invention resides in
the optical element according to the first to the fourth features,
wherein each cell has a phase-modulating part provided with an
optical path length corresponding to a specific phase.
[0014] (7) The seventh feature of the present invention resides in
the optical element according to the first feature, wherein each
cell has a concave part formed by hollowing a part provided with an
area corresponding to a specific amplitude by a depth corresponding
to a specific phase.
[0015] (8) The eighth feature of the present invention resides in
the optical element according to the first feature, wherein each
cell has a convex part formed by protruding a part provided with an
area corresponding to a specific amplitude by a height
corresponding to a specific phase.
[0016] (9) The ninth feature of the present invention resides in
the optical element according to the seventh or eighth feature,
wherein a surface where the concave part or the convex part of each
cell is formed serves as a reflecting surface, and incident light
provided to the cell is reflected by the reflecting surface and
thereby turns into emission light.
[0017] (10) The tenth feature of the present invention resides in
the optical element according to the seventh or eighth feature,
wherein each cell includes a main body layer having a concave part
or a convex part and a protective layer with which a surface where
the concave part or the convex part of the main body layer is
formed is covered, and the main body layer and the protective layer
are made of materials different from each other.
[0018] (11) The eleventh feature of the present invention resides
in the optical element according to the tenth feature, wherein the
main body layer and the protective layer are made of transparent
materials different in a refractive index from each other, and
incident light provided to the cell passes through the main body
layer and the protective layer and thereby turns into emission
light.
[0019] (12) The twelfth feature of the present invention resides in
the optical element according to the tenth feature, wherein a
boundary between the main body layer and the protective layer forms
a reflecting surface, and incident light provided to the cell is
reflected by the reflecting surface and thereby turns into emission
light.
[0020] (13) The thirteenth feature of the present invention resides
in the optical element according to the first to the twelfth
features, wherein each cell is arranged one-dimensionally or
two-dimensionally.
[0021] (14) The fourteenth feature of the present invention resides
in the optical element according to the thirteenth feature, wherein
a longitudinal pitch of each cell and a lateral pitch of each cell
are arranged so as to be an equal pitch.
[0022] (15) The fifteenth feature of the present invention resides
in the optical element according to the first to the fourteenth
features, wherein a complex amplitude distribution of object light
from an object image is recorded so that the object image is
reconstructed when observed from a predetermined viewing point so
as to be usable as a hologram.
[0023] (16) The sixteenth feature of the present invention resides
in a method for manufacturing an optical element where a
predetermined object image is recorded, the method comprising:
[0024] a cell defining step of defining a set of a plurality of
three-dimensional virtual cells;
[0025] a representative-point defining step of defining a
representative point for each virtual cell;
[0026] an object image defining step of defining an object image to
be recorded;
[0027] an amplitude phase defining step of defining a specific
amplitude and a specific phase in each virtual cell by calculating
a complex amplitude at a position of each representative point of
object light emitted from the object image; and
[0028] a physical cell forming step of replacing each virtual cell
with a real physical cell and forming an optical element that
consists of a set of three-dimensional physical cells;
[0029] wherein, at the physical cell forming step, when
predetermined incident light is given to each physical cell,
replacement is carried out by each physical cell having a specific
optical property so as to obtain emission light that has changed an
amplitude and a phase of the incident light in accordance with a
specific amplitude and a specific phase defined in the virtual cell
corresponding to the physical cell.
[0030] (17) The seventeenth feature of the present invention
resides in the manufacturing method for the optical element
according to the sixteenth feature, wherein at the cell defining
step, a cell set is defined by arranging block-like virtual cells
one-dimensionally or two-dimensionally.
[0031] (18) The eighteenth feature of the present invention resides
in the manufacturing method for the optical element according to
the sixteenth or seventeenth feature, wherein at the amplitude
phase defining step, a plurality of point light sources are defined
on the object image, and object light of a spherical wave having a
predetermined amplitude and a predetermined phase is regarded as
being emitted from each point light source, and a totaled complex
amplitude of the object light from the point light sources at a
position of each representative point is calculated at a
predetermined standard time.
[0032] (19) The nineteenth feature of the present invention resides
in the manufacturing method for the optical element according to
the eighteenth feature, wherein K point light sources that emit
object light whose wavelength is .lambda. are defined on the object
image, and if an amplitude of object light emitted from a k-th
point light source O(k) (k=1 to K) is represented as Ak, and a
phase thereof is represented as .theta. k, and a distance between a
predetermined representative point P and the k-th point light
source O(k) is represented as rk, a totaled complex amplitude of
the object light from the K point light sources at the
predetermined representative point P is calculated as follows:
.SIGMA..sub.(k=1,K)(Ak/rk.multidot.cos (.theta. k.+-.2
.pi.rk/.lambda.) +iAk/rk.multidot.sin (.theta. k.+-.2
.pi.rk/.lambda.)).
[0033] (20) The twentieth feature of the present invention resides
in the manufacturing method for the optical element according to
the sixteenth to nineteenth features, wherein, at the physical cell
forming step, each virtual cell is replaced with a physical cell
having a concave part formed by hollowing a part provided with an
area corresponding to a specific amplitude by a depth corresponding
to a specific phase.
[0034] (21) The twenty-first feature of the present invention
resides in the manufacturing method for the optical element
according to the sixteenth to nineteenth features, wherein, at the
physical cell forming step, each virtual cell is replaced with a
physical cell having a convex part formed by protruding a part
provided with an area corresponding to a specific amplitude by a
height corresponding to a specific phase.
[0035] (22) The twenty-second feature of the present invention
resides in the manufacturing method for the optical element
according to the twentieth or twenty-first feature, wherein:
[0036] a refractive index of a material filled in the concave part
of the physical cell or a material that constitutes the convex part
is represented as n1,
[0037] a refractive index of another material in contact with the
material n1 is represented as n2,
[0038] a wavelength of object light is represented as .lambda.,
[0039] a maximum depth dmax of the concave part or a maximum height
dmax of the convex part is set to be dmax
=.lambda./.vertline.n1-n2.vertline.,
[0040] a depth or height d corresponding to a specific phase
.theta. is determined by the expression
d=.lambda..multidot..theta./2(n1-n2).pi. when n1>n2, and is
determined by the expression d=dmax
-.lambda..multidot..theta./2(n2-n1).pi. when n1<n2, and
[0041] an object image is reconstructed by transmission light that
has passed through the concave part or the convex part.
[0042] (23) The twenty-third feature of the present invention
resides in the manufacturing method for the optical element
according to the twentieth or twenty-first feature, wherein:
[0043] a refractive index of a material filled in the concave part
of the physical cell or a material that constitutes the convex part
is represented as n, a wavelength of object light is represented as
.lambda.,
[0044] a maximum depth of the concave part or a maximum height dmax
of the convex part is set to be dmax=.lambda./2n,
[0045] a depth or a height d corresponding to the specific phase
.theta. is determined by the expression
d=.lambda..multidot..theta./4n.pi.,
[0046] and
[0047] an object image is reconstructed by reflected light that has
been reflected by the boundary of the concave part or the convex
part.
[0048] (24) The twenty-fourth feature of the present invention
resides in the manufacturing method for the optical element
according to the twentieth to twenty-third features, wherein
.alpha. kinds of a plurality of areas are defined as areas
corresponding to a specific amplitude, .beta. kinds of a plurality
of depths or heights are defined as depths or heights corresponding
to a specific phase so as to prepare .alpha..times..beta. kinds of
physical cells in total, and each virtual cell is replaced with a
physical cell closest in a necessary optical property among said
physical cells.
[0049] (25) The twenty-fifth feature of the present invention
resides in the manufacturing method for the optical element
according to the sixteenth to twenty-fourth features, further
comprising a phase-correcting step of correcting the specific phase
defined for each virtual cell in consideration of a direction of
illumination light projected when reconstructed or in consideration
of a position of a viewing point when reconstructed.
[0050] (26) The twenty-fifth feature of the present invention
resides in the manufacturing method for the optical element
according to the sixteenth to twenty-fifth features, wherein:
[0051] at the cell defining step, a cell set of virtual cells
arranged on a two-dimensional matrix is defined by arranging the
virtual cells horizontally and vertically,
[0052] at the amplitude phase defining step, a plurality of M point
light source rows that are each extended in a horizontal direction
and are mutually disposed in a vertical direction are defined on an
object image, and M groups in total are defined by defining virtual
cells that belong to a plurality of rows contiguous in the vertical
direction in the two-dimensional matrix as one group,
[0053] the M point light source rows and the M groups are caused to
correspond to each other in accordance with an arrangement order
relative to the vertical direction, and
[0054] a totaled complex amplitude at a position of each
representative point is calculated on a supposition that object
light emitted from a point light source in an m-th point light
source row (m=1 to M) reaches only virtual cells that belongs to an
m-th group.
BRIEF DESCRIPTION OF THE DRAWINGS
[0055] FIG. 1 is a perspective view showing general holography for
optically recording an object image as interference fringes by use
of reference light.
[0056] FIG. 2 is a perspective view showing the amplitude and phase
of object light that has reached a representative point P(x, y) on
a recording surface 20 when a point light source O and the
recording surface 20 are defined.
[0057] FIG. 3 is a perspective view showing the complex amplitude
of object light at the position of the representative point P(x, y)
when the object light emitted from each point light source on an
object image 10 has reached the representative point P(x, y) on the
recording surface 20.
[0058] FIG. 4 shows the calculation of an amplitude A (x, y) and a
phase .theta. (x, y) on the basis of a complex amplitude shown by a
coordinate point Q on a complex coordinate plane.
[0059] FIG. 5 is a perspective view showing one example of a
three-dimensional virtual cell set 30 defined to record the object
image 10.
[0060] FIG. 6 shows the function of the amplitude modulation and
phase modulation of a three-dimensional cell C(x, y) used in the
present invention.
[0061] FIG. 7 shows one example of 16 kinds of physical cells
different in transmittance and in refractive index that are to be
the constituent parts of an optical element according to the
present invention.
[0062] FIG. 8 is a perspective view showing one example of the
structure of a physical cell C(x, y) considered most suitable for
use in the present invention.
[0063] FIG. 9 is a front view for explaining a reason why amplitude
information is recorded as a width G1 of a groove G(x, y) and phase
information is recorded as a depth G2 of the groove G(x, y) when
the physical cell C(x, y) shown in FIG. 8 is used as a transmission
type cell.
[0064] FIG. 10 is a front view for explaining a reason why
amplitude information is recorded as the width G1 of the groove
G(x, y) and phase information is recorded as the depth G2 of the
groove G(x, y) when the physical cell C(x, y) shown in FIG. 8 is
used as a reflection type cell.
[0065] FIG. 11 is a perspective view showing an example in which
seven kinds of groove widths and four kinds of depths are
determined so that 28 kinds of physical cells in total are prepared
in the structure of the physical cell C(x, y) shown in FIG. 8.
[0066] FIG. 12 shows the relationship between the refractive index
and the groove depth of each part for the transmission type cell
C(x, y).
[0067] FIG. 13 shows the relationship between the refractive index
and the groove depth of each part for the reflection type cell C(x,
y).
[0068] FIG. 14 is a side view showing a basic form in which
reconstructing illumination light is projected from a normal
direction onto the optical element of the present invention, and an
object image recorded as a hologram is observed from the normal
direction.
[0069] FIG. 15 is a side view showing a form in which
reconstructing illumination light is projected from an oblique
direction onto the optical element of the present invention, and an
object image recorded as a hologram is observed from the normal
direction.
[0070] FIG. 16 is a side view showing a form in which
reconstructing illumination light is projected from the normal
direction onto the optical element of the present invention, and an
object image recorded as a hologram is observed from the oblique
direction.
[0071] FIG. 17 is a side view showing a principle according to
which specific phase is subjected to corrective processing in order
to make an optical element that corresponds to a reconstructing
environment shown in FIG. 15.
[0072] FIG. 18 is a side view showing a principle according to
which specific phase is subjected to corrective processing in order
to make an optical element that corresponds to a reconstructing
environment shown in FIG. 16.
[0073] FIG. 19 is a perspective view showing a technique for making
an optical element that corresponds to a reconstructing environment
in which white reconstructing illumination light is used.
[0074] FIG. 20 is a perspective view showing an example in which
three-dimensional cells are arranged like a one-dimensional matrix
so as to construct a three-dimensional virtual cell set 30.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0075] The present invention will be hereinafter described on the
basis of the embodiments shown in the figures.
[0076] .sctn. 1. Basic Principle of the Present Invention
[0077] FIG. 1 is a perspective view that shows general holography
in which an object image is optically recorded as interference
fringes by use of reference light. When a stereoscopic image of an
object 10 is recorded onto a recording medium 20, the object 10 is
illuminated with light (normally, with a laser beam) having the
same wavelength as reference light R, and interference fringes
formed by object light from the object 10 and the reference light R
on the recording medium 20 are recorded. Herein, if an XY
coordinate system is defined on the recording medium 20, and
attention is paid to an arbitrary point P(x, y) located at
coordinates (x, y), the amplitude intensity of a composite wave
resulting from interference between each object light from each
point O(1), O(2), . . . ,O(k), . . . ,O(K) located on the object 10
and the reference light R will be recorded onto the point P(x, y).
Likewise, the amplitude intensity of the composite wave resulting
from the interference between the object light from each point and
the reference light R will be recorded onto another point P(x',y')
on the recording medium 20. However, since a difference in the
propagation distance of light exists, the amplitude intensity
recorded onto the point P(x, y) and the amplitude intensity
recorded onto the point P(x',y') are different from each other. As
a result, an amplitude intensity distribution is recorded onto the
recording medium 20, and the amplitude and phase of the object
light are expressed by this amplitude intensity distribution. When
reconstructed, reconstructing illumination light having the same
wavelength as the reference light R is projected from the same
direction as that of the reference light R (or, alternatively, from
a direction that has a plane symmetry with respect to the recording
medium 20), and thus a stereoscopic reconstructed image of the
object 10 is obtained.
[0078] In order to record interference fringes onto the recording
medium 20 according to an optical method, a photosensitive material
is used as the recording medium 20, and interference fringes are
recorded as a light and dark pattern on the recording medium 20. On
the other hand, if the computer-generated hologram method is used,
a phenomenon occurring in the optical system shown in FIG. 1
requires simulation on a computer. Specifically, the object image
10 and the recording surface 20 are defined in a virtual
three-dimensional space on the computer instead of the real object
10 or the real recording medium 20, and many point light sources
O(1), O(2), . . . ,O(k), . . . ,O(K) are defined on the object
image 10. Further, object light (i.e., spherical wave) with a
predetermined wavelength, amplitude, and phase is defined for each
point light source, and reference light with the same wavelength as
the object light is defined. On the other hand, many representative
points P(x, y) are defined on the recording surface 20, and the
amplitude intensity of a composite wave of both the object light
and the reference light that reach the position of each
representative point is calculated. Since an amplitude intensity
distribution (i.e., interference fringes) is obtained on the
recording surface 20 by computation, a physical hologram recording
medium can be formed if the amplitude intensity distribution is
recorded onto the physical recording medium in the form of a
light/dark distribution or as a concave/convex distribution.
[0079] In fact, the interference fringes are not necessarily
required to be recorded by using the reference light R if the
computer-generated hologram method is used. It is also possible to
record the object light from the object image 10 directly onto the
recording surface 20. In more detail, when a hologram is optically
generated, it is necessary to generate an interference wave on the
recording medium 20 made of a photosensitive material during a
fixed period of time needed for exposure and to record this wave as
interference fringes. Therefore, it is necessary to generate an
interference wave that turns to a standing wave by use of reference
light. However, if the computer-generated hologram method is used,
the state of the wave at a certain moment that exists on the
recording surface 20 can be observed in such a way as if a lapse in
time is stopped, and this wave can be recorded. In other words, the
amplitude and phase of the object light at the position of each
representative point on the recording surface 20 at a predetermined
standard time can be obtained by calculation. In the present
invention, this advantage in a computer-generated hologram is
employed, and the method for directly recording the amplitude and
phase of the object light is used without using the method for
recording the object light as interference fringes resulting from
cooperation with the reference light.
[0080] Now let us consider how the amplitude and phase of the
object light that has reached the representative point P(x, y) on
the recording surface 20 are calculated when the point light source
O and the recording surface 20 are defined as shown in, for
example, the perspective view of FIG. 2. Generally, a wave motion
in consideration of the amplitude and the phase is expressed by the
following function of complex variable (i is an imaginary
unit):
A cos .theta.+i A sin .theta.
[0081] Herein, A is a parameter showing the amplitude, and .theta.
is a parameter showing the phase. Accordingly, if object light
emitted from a point light source O is defined by the function A
cos .theta.+i A sin .theta., the object light at the position of a
representative point P(x, y) is expressed by the following function
of the complex variable:
A/r cos (.theta.+2 .pi.r/.lambda.)+i A/r sin (.theta.+2
.pi.r/.lambda.)
[0082] Herein, r is a distance between the point light source 0 and
the representative point P(x, y), and .lambda. is a wavelength of
the object light. The amplitude of the object light attenuates as
the distance r becomes greater, and the phase depends on the
distance r and the wavelength .lambda.. This function does not have
variables that indicate time. The reason is that this function is
an expression showing the momentary state of a wave observed when a
lapse in time is stopped at a predetermined standard time as
described above.
[0083] Accordingly, in order to record information for the object
image 10 onto the recording surface 20, many point light sources
O(1), O(2), . . . , O(k), . . . , O(K) are defined on the object
image 10 as shown in the perspective view of FIG. 3, and then the
amplitude and phase of a composite wave of the object light emitted
from each point light source are calculated at the position of each
representative point on the recording surface 20, and the
calculation result is recorded by a certain method. Let us now
suppose that K point light sources in total are defined on the
object image 10, and the object light emitted from the k-th ("-th"
is a suffix indicating an ordinal number) point light source O(k)
is expressed by the following function of the complex variable as
shown in FIG. 3:
Ak cos .theta.k+i Ak sin .theta.k
[0084] If the object image 10 is constructed of a set of pixels
each of which has a predetermined gradation value (concentration
value), the parameter Ak showing the amplitude is fixed in
accordance with the gradation value of a pixel which exists at the
position of the point light source O(k). The phase .theta.k is
allowed to be defined generally as .theta.k=0. However, it is also
possible to create such a setting as to emit object light rays
different in phase from each part of the object image 10 if
necessary. When the object light expressed by the above function
can be defined for each of all the K point light sources, the
composite wave of all the K object light at the position of an
arbitrary representative point P(x, y) on the recording surface 20
is expressed by the following function of the complex variable as
shown in FIG. 3:
.SIGMA..sub.k=1,K(Ak/rk cos (.theta.k+2 .pi.rk/.lambda.) +i Ak/rk
sin (.theta.k+2 .pi.rk/.lambda.)
[0085] Herein, rk is the distance between the k-th point light
source O(k) and the representative point P(x, y). The above
function corresponds to an expression that is used when the object
image 10 is reconstructed at the back of the recording medium. When
the object image 10 is reconstructed to rise to the front side of
the recording medium, the function of the complex variable is
merely calculated according to the following expression (note that
the reference character in the term of the phase is negative):
.SIGMA..sub.k=1,K(Ak/rk cos (.theta.k-2 .pi.rk/.lambda.) +i Ak/rk
sin (.theta.k-2 .pi.rk/.lambda.)
[0086] Therefore, the function of the complex variable in
consideration of both situations is as follows:
.SIGMA..sub.k=1,K(Ak/rk cos (.theta.k.+-.2 .pi.rk/.lambda.) +i
Ak/rk sin (.theta.k.+-.2 .pi.rk/.lambda.)
[0087] If the form of Rxy+iIxy is taken under the condition that
the real number part of this function is Rxy and the imaginary
number part thereof is Ixy, the complex amplitude (i.e., amplitude
in consideration of the phase) at the position of the
representative point P(x, y) of this composite wave is shown by a
coordinate point Q on the complex coordinate plane as shown in FIG.
4. After all, the amplitude of the composite wave of the object
light at the representative point P(x, y) is given by the distance
A(x, y) between the origin O and the coordinate point Q on the
coordinate plane shown in FIG. 4, and the phase is given by the
angle .theta.(x, y) between the vector OQ and the real number
axis.
[0088] Thus, the amplitude A(x, y) and phase .theta.(x, y) of the
composite wave of the object light at the position of the arbitrary
representative point P(x, y) defined on the recording surface 20 is
obtained by computation. Accordingly, the complex amplitude
distribution (i.e., distribution of the amplitude and phase of the
object-light-composite wave) of the object light emitted from the
object image 10 is obtained on the recording surface 20. As a
result, the object image 10 can be recorded as a hologram if the
complex-amplitude distribution obtained in this way is recorded on
a physical recording medium in some way so that the wave front of
the object light is to be reconstructed and then predetermined
reconstructing illumination light is given.
[0089] In order to record a complex amplitude distribution of
object light emitted from the object image 10 onto the recording
surface 20, the present inventor has conceived a method for using
three-dimensional cells. The following procedure should be carried
out to record a complex amplitude distribution by use of
three-dimensional cells and record the object image 10 as a
hologram. First, a three-dimensional virtual cell set 30 is defined
at the position of the recording surface 20 as shown in FIG. 5, for
example. The three-dimensional virtual cell set 30 is constructed
by vertically and horizontally arranging block-like virtual cells
each of which has a predetermined size so as to place the cells
two-dimensionally. Thereafter, the representative point of each
virtual cell is defined. The position of the representative point
may be one arbitrary point in the cell. In this case, the
representative point of the cell is defined at the position of the
center point on the front surface of the cell (i.e., surface facing
the object image 10). For example, if an XY coordinate system is
defined on the front surface of the three-dimensional virtual cell
set 30 (i.e., on the surface facing the object image 10), and a
virtual cell having the representative point P(x, y) located at the
position of coordinates (x, y) in this coordinate system is called
a virtual cell C(x, y), the representative point P(x, y) will
occupy the center point of the front surface of this virtual cell
C(x, y).
[0090] On the other hand, the object image 10 is defined as a set
of point light sources. In the example of FIG. 5, the object image
10 is defined as a set of K point light sources O(1), O(2), . . . ,
O(k), . . . , O(K). Object light having predetermined amplitude and
phase is emitted from each point light source, and a composite wave
of these object light rays reaches the representative point P(x,
y). The complex amplitude of this composite wave can be calculated
according to the above-mentioned expressions and can be shown as a
coordinate point Q on the complex coordinate plane shown in FIG. 4,
and, based on this coordinate point Q, the amplitude A(x, y) and
phase .theta.(x, y) are obtained, as described above. Herein, the
amplitude A(x, y) and phase .theta.(x, y) obtained for the
representative point P(x, y) will be called a specific amplitude
A(x, y) and a specific phase .theta.(x, y) for the virtual cell
C(x, y) including the representative point P(x, y).
[0091] The above-mentioned procedure is practically carried out as
arithmetic processing by use of a computer. Accordingly, concerning
each of all the virtual cells that make up the three-dimensional
virtual cell set 30, a specific amplitude and a specific phase can
be obtained by this arithmetic processing. Therefore, an optical
element (i.e., a hologram recording medium in which the object
image 10 is recorded) that is made up of a set of three-dimensional
physical cells can be formed by replacing these virtual cells with
real physical cells, respectively. Herein, the physical cell to be
replaced with the virtual cell must have optical properties by
which the amplitude and phase of incidence light can be modulated
in accordance with the specific amplitude and specific phase
defined in the virtual cell. In other words, when predetermined
incidence light is given, the replaced individual physical cell
must have the specific optical properties of having a function to
generate emission light by changing the amplitude and phase of the
incidence light in accordance with the specific amplitude and
specific phase that have been defined in the virtual cell before
replacement.
[0092] When predetermined reconstructing illumination light
(ideally, a plane wave of monochromatic light with the same
wavelength as the wavelength .lambda. of the object light used in
the above-mentioned arithmetic processing) is projected onto the
optical element made up of a set of physical cells having the
specific optical properties, the reconstructing illumination light
is modulated by the specific amplitude and the specific phase in
each physical cell. Therefore, the original wave front of the
object light is reconstructed. As a result, the hologram recorded
in this optical element is reconstructed.
[0093] .sctn. 2. Concrete Structure of Physical Cell
[0094] Next, the concrete structure of a physical cell used in the
present invention will be described. A physical cell used in the
present invention is a three-dimensional stereo-cell, and its
specific amplitude and its specific phase are defined. Any type of
cell can be used if it has such a specific optical property that
emission light in which the amplitude and phase of predetermined
incidence light are changed in accordance with the specific
amplitude and specific phase defined in the cell can be obtained
when the incidence light is given to the cell. For example, in a
case in which an amplitude A(x, y) and a phase .theta.(x, y) is
recorded for a three-dimensional cell C(x, y) shown in FIG. 6, and
incidence light Lin whose amplitude is Ain and whose phase is
.theta. in is given to this cell, all that is needed is to obtain
emission light Lout whose amplitude Aout equals Ain A(x, y) and
whose phase .theta. out equals .theta. in .+-..theta.(x, y). The
amplitude Ain of the incidence light undergoes modulation by the
specific amplitude A(x, y) recorded on the cell and changes into
the amplitude Aout, whereas the phase .theta. in of the incidence
light undergoes modulation by the specific phase .theta.(x, y)
recorded on the cell and changes into the phase .theta. out.
[0095] One method for modulating the amplitude in the
three-dimensional cell is to provide an amplitude-modulating part
having transmittance that corresponds to the specific amplitude in
the cell (the entire cell may be used as the amplitude-modulating
part, or the amplitude-modulating part may be provided to a part of
the cell). For example, a cell provided with the
amplitude-modulating part whose transmittance is Z% serves as a
cell in which the specific amplitude of A(x, y) equal to Z/100 is
recorded, and, when incidence light with the amplitude Ain passes
through this cell, it is subjected to amplitude modulation by
emission light whose amplitude Aout equals Ain.multidot.Z/100. One
possible method for setting the transmittance of each
three-dimensional cell at an arbitrary value is to, for example,
change the content of a coloring agent for each cell.
[0096] Another method for modulating the amplitude in the
three-dimensional cell is to provide an amplitude-modulating part
having reflectivity that corresponds to the specific amplitude in
the cell. For example, a cell provided with the
amplitude-modulating part whose reflectivity is Z% serves as a cell
in which the specific amplitude of A(x, y) equal to Z/100 is
recorded, and, when incidence light with the amplitude Ain is
reflected by this amplitude-modulating part and is emitted, it is
subjected to amplitude modulation by emission light whose amplitude
Aout equals Ain.multidot.Z/100. One possible method for setting the
reflectivity of each three-dimensional cell at an arbitrary value
is to, for example, prepare a reflecting surface in the cell (this
reflecting surface serves as the amplitude-modulating part) and set
the reflectivity of the reflecting surface at an arbitrary value.
More specifically, the ratio of reflected light to scattered light
can be adjusted by, for example, changing the surface roughness of
the reflecting surface, and therefore the adjustment of the surface
roughness makes it possible to prepare a cell having arbitrary
reflectivity.
[0097] Still another method for modulating the amplitude in the
three-dimensional cell is to provide an amplitude-modulating part
having an effective area that corresponds to the specific amplitude
in the cell. For example, if it is assumed that the area of all the
incident region of incidence light is 100%, a cell having an
amplitude-modulating part constructed such that emission light
effective for reconstructing an object image can be obtained only
from incidence light that has struck a part having a Z% effective
area thereof serves as a cell in which the specific amplitude of
A(x, y)=Z/100 is recorded. That is, even if incidence light having
the amplitude Ain strikes the amplitude-modulating part, only Z% of
the light goes out as effective emission light, and therefore it is
subjected to amplitude modulation by emission light having the
amplitude of Aout =Ain.multidot.Z/100. One possible method for
obtaining effective emission light only from a region having such a
specific effective area is to use a cell having a physical
concave/convex structure. A concrete example thereof will be
described in .sctn. 3.
[0098] On the other hand, one method for modulating the phase in
the three-dimensional cell is to provide a phase-modulating part
having a refractive index that corresponds to the specific phase in
the cell (the entire cell can be used as the phase-modulating part,
or the phase-modulating part can be provided to a part of the
cell). For example, even if incidence light with the same phase is
given, a difference in the phase of emission light arises between a
cell provided with the phase-modulating part made of a material
whose refractive index is n1 and a cell provided with the
phase-modulating part made of a material whose refractive index is
n2. Therefore, arbitrary phase modulation can be applied to the
incidence light by constructing the cell made of various materials
with different refractive indexes.
[0099] Another method for modulating the phase in the
three-dimensional cell is to provide a phase-modulating part having
an optical path length that corresponds to the specific phase in
the cell (the entire cell can be used as the phase-modulating part,
or the phase-modulating part can be provided to a part of the
cell). For example, even if the cell has a phase-modulating part
made of the same material whose refractive index is n, a difference
in the phase of each emission light will arise if the optical path
length of the phase-modulating part is different regardless of the
fact that incidence light with the same phase is given. For
example, if the optical path length of the phase-modulating part
provided in a first cell is L, and the optical path length of the
phase-modulating part provided in a second cell is 2L, the distance
by which emission light emitted from the second cell travels
through the material whose refractive index is n is twice as long
as in the case of emission light emitted from the first cell even
if incidence light with the same phase is given. Therefore, such a
great phase difference arises. A method for realizing a
phase-modulating part with an arbitrary optical path length is to
use a cell having a physical concave/convex structure. A concrete
example thereof will be described in .sctn. 3.
[0100] A three-dimensional cell having an amplitude modulating
function based on a specific amplitude or a three-dimensional cell
having a phase modulating function based on a specific phase can be
realized by some of the methods described above, and an optical
element according to the present invention can be realized by
selecting an arbitrary method from among the amplitude modulating
methods and the phase modulating methods mentioned above. For
example, if a method in which an amplitude-modulating part with
transmittance that corresponds to a specific amplitude is provided
in the cell is employed as the amplitude modulating method, and a
method in which a phase-modulating part with a refractive index
that corresponds to a specific phase is provided in the cell is
employed as the phase modulating method, and the entire cell is
used as the amplitude-modulating part and as the phase-modulating
part, an optical element can be formed by selectively arranging 16
kinds of physical cells shown in the table of FIG. 7. The
horizontal axis of this table indicates amplitude A, and the
vertical axis thereof indicates phase .theta.. The amplitude A and
the phase .theta. are each divided into four ranges.
[0101] Herein, the cells (i.e., cells of the first column in the
table) depicted in a range in which the amplitude A corresponds to
"0-25%" are ones that are each made of a material whose
transmittance is very low, the cells (i.e., cells of the second
column in the table) depicted in a range in which the amplitude A
corresponds to "25-50%" are ones that are each made of a material
whose transmittance is slightly low, the cells (i.e., cells of the
third column in the table) depicted in a range in which the
amplitude A corresponds to "50-75%" are ones that are each made of
a material whose transmittance is slightly high, and the cells
(i.e., cells of the fourth column in the table) depicted in a range
in which the amplitude A corresponds to "75-100%" are ones that are
each made of a material whose transmittance is very high. On the
other hand, the cells (i.e., cells of the first row in the table)
depicted in a range in which the phase .theta. corresponds to
"0-.pi./2" are ones that are each made of a material whose
refractive index n1 is very close to that of air, the cells (i.e.,
cells of the second row in the table) depicted in a range in which
the phase 0 corresponds to ".pi./2-.pi." are ones that are each
made of a material whose refractive index n2 is slightly greater
than that of air, the cells (i.e., cells of the third row in the
table) depicted in a range in which the phase .theta. corresponds
to ".pi.-3 .pi./2" are ones that are each made of a material whose
refractive index n3 is much greater than that of air, and the cells
(i.e., cells of the fourth row in the table) depicted in a range in
which the phase .theta. corresponds to "3 .pi./2-2 .pi." are ones
that are each made of a material whose refractive index n4 is very
much greater than that of air.
[0102] In the example of FIG. 7, sixteen cells in total with four
kinds of transmittances and four kinds of refractive indexes are
prepared as described above. A desirable way of recording the
amplitude and phase in the cell with higher accuracy is to set the
transmittance steps and the refractive-index steps in more detail
and prepare even more kinds of cells. What is needed to replace the
virtual cells by use of these sixteen kinds of physical cells is to
select a physical cell that has optical properties closest in the
optical properties needed to carry out modulation based on the
specific amplitude and the specific phase defined in each virtual
cell.
[0103] .sctn. 3. Practical Structure of Physical Cell
[0104] If physical cells used in the present invention are cells
that have a function to modulate incidence light in accordance with
a specific amplitude and a specific phase as described above, any
kind of cell structure is allowed to embody the present invention.
FIG. 7 shows an example in which the modulation according to a
specific amplitude is controlled by the transmittance, and the
modulation according to a specific phase is controlled by the
refractive index. Theoretically, many methods exist to modulate the
amplitude or the phase as described above. However, from the
viewpoint of industrial mass production, all the methods are not
necessarily practical. In order to reconstruct an object image that
has a certain degree of resolution by using the optical element
according to the present invention, the size of each
three-dimensional cell must be determined to be less than a
criterion (roughly speaking, when the size of a cell exceeds 100
.mu.m, it is difficult to reconstruct a satisfactorily discernible
object image). Therefore, it is need to two-dimensionally arrange
small cells as a component if sixteen kinds of physical cells shown
in FIG. 7 are combined to form an optical element, and,
additionally, there is a need to dispose a specific cell of the
sixteen kinds of cells at a specific position. From this fact, it
can be found that the method for constructing the optical element
using the physical cells shown in FIG. 7 is unsuitable for
industrial mass production.
[0105] As a method in which amplitude information and phase
information can be given to a single physical cell and an optical
element suitable for industrial mass production is constructed with
a set of such physical cells, the present inventor has contrived a
method for giving a concave/convex structure to each physical cell,
then recording amplitude information as the area of this
concave/convex structure part, and recording phase information as a
level difference (i.e., depth of a concave part or height of a
convex part) in the concave/convex structure part.
[0106] FIG. 8 is a perspective view showing an example of the
structure of a physical cell C(x, y) that can be regarded as most
suitable for use in the present invention. As shown in the figure,
this three-dimensional physical cell has an almost rectangular
solid block shape, and a groove G(x, y) is formed in the upper
surface thereof. In this example, the size of the physical cell
C(x, y), C1=0.6 .mu.m, C2=0.25 .mu.m, and C3=0.25 .mu.m, and the
size of the groove G(x, y), G1=0.2 .mu.m, G2=0.05 .mu.m, and
G3=C3=0.25 .mu.m are shown in the figure. The use of the thus
constructed physical cell C(x, y) makes it possible to record the
amplitude information as a value of the lateral width G1 of the
groove G(x, y) and record the phase information as a value of the
depth G2 of the groove G(x, y). In other words, when a virtual cell
in which a specific amplitude and a specific phase are defined is
replaced with the thus constructed physical cell, the replacement
is carried out by the physical cell having the size G1
corresponding to the specific amplitude and having the size G2
corresponding to the specific phase.
[0107] With reference to the front view of FIG. 9, a description
will be provided of the reason why the amplitude information is
recorded as the width G1 of the groove G(x, y) and the phase
information is recorded as the depth G2 of the groove G(x, y) in
the physical cell shown in FIG. 8. Let us now suppose that the
physical cell C(x, y) is made of a material with the refractive
index n2, and the part outside the physical cell C(x, y) is made of
a material (e.g., air) with the refractive index n1. In this case,
when the optical path length passing through the medium with the
refractive index n2 is compared between incident light L1 that has
struck vertically the inner surface S1 of the groove G(x, y) and
incident light L2 that has struck vertically the outer surface S2
of the groove G(x, y), it can be found that the optical path length
of the light L1 is shorter than that of the light L2 by the depth
G2 of the groove G(x, y). Therefore, if the refractive indexes n1
and n2 are different from each other, a predetermined phase
difference will arise between the light L1 and the light L2 emitted
from the physical cell C(x, y) as transmission light.
[0108] On the other hand, FIG. 10 is a front view showing a case in
which emission light is obtained as reflected light from the
physical cell C(x, y). In this example, the upper surface of the
physical cell C(x, y), i.e., surfaces S1 and S2 are
reflecting-surfaces, and the incident light L1 that has struck
almost vertically the inner surface S1 of the groove G(x, y) and
the incident light L2 that has struck almost vertically the outer
surface S2 of the groove G(x, y) are reflected by the respective
surfaces almost vertically and emitted therefrom. At this time, it
can be found that, when the entire optical path length along the
path of the incidence and reflection is compared, the optical path
length of the light L1 becomes longer than that of the light L2 by
double the depth G2 of the groove G(x, y). Therefore, a
predetermined phase difference arises between the light L1 and the
light L2 emitted from the physical cell C(x, y) as reflected
light.
[0109] Accordingly, even if the physical cell C(x, y) is a
transmission type cell or a reflection type cell, a predetermined
phase difference arises between the incident light L1 that has
struck the inner surface S1 of the groove G(x, y) and the incident
light L2 that has struck the outer surface S2 of the groove G(x,
y). This phase difference depends on the depth G2 of the groove
G(x, y). Therefore, if only the emission light obtained on the
basis of the incidence light that has struck the inner surface Si
of the groove G(x, y) among the incident light rays that have
struck the upper surface of the physical cell C(x, y) is treated as
emission light effective for the reconstruction of the object image
10 (in other words, if only the light L1 is treated as emission
light effective for the reconstruction of the image in FIG. 9 or
FIG. 10), emission light L1 effective for the image reconstruction
resultantly undergoes phase modulation by a specific phase that
corresponds to the depth G2 of the groove G(x, y) in this physical
cell C(x, y). Thus, the phase information of the object light can
be recorded as the depth G2 of the groove G(x, y).
[0110] Further, if only the emission light obtained on the basis of
the incidence light that has struck the inner surface S1 of the
groove G(x, y) is treated as emission light effective for the
reconstruction of the object image 10 as mentioned above, the
amplitude information of the object light can be recorded as the
width G1 of the groove G(x, y). The reason is that the area of the
inner surface Si of the groove G(x, y) enlarges, and the percentage
of the emission light effective for the reconstruction of the
object image 10 increases as the width Gi of the groove G(x, y)
becomes greater. That is, since the emission light L2 shown in FIG.
9 or FIG. 10 does not include any significant phase components, the
emission light is merely observed as a noise component of a
so-called background, and is not recognized as light effective for
reconstructing a significant image even if the emission light L2 is
observed at a viewing position when reconstructed. By contrast,
since the emission light L1 includes significant phase components,
it is observed as a signal component effective for image
reconstruction. After all, the width G1 of the groove G(x, y)
becomes a factor for determining the ratio of the light L1 observed
as a signal component among the light rays emitted from the
physical cell C(x, y), and becomes a parameter for giving the
amplitude information of the signal wave.
[0111] Generally, the amplitude information is not expressed by the
width G1 of the groove G(x, y), but by the area of the inner
surface S1 of the groove G(x, y). In the embodiment shown in FIG.
8, since the length G3 of the groove G(x, y) happens to be set to
be always equal to the length C3 of the physical cell C(x, y), the
area of the inner surface S1 of the groove G(x, y) is proportional
to the extent of the width G1. However, the length G3 of the groove
G(x, y) does not necessarily need to be fixed, and both of the
width and the length may be changed so that the area of the inner
surface S1 of the groove G(x, y) has variations.
[0112] If a part having an area corresponding to the specific
amplitude (i.e., a part corresponding to the surface S1 of FIG. 8)
of the upper surface of the block-like physical cell is hollowed by
the depth corresponding to the specific phase (i.e., depth
corresponding to the dimension G2 of FIG. 8) so as to form a
concave part (i.e., groove G(x, y)) in this way, the amplitude
modulation corresponding to the specific amplitude and the phase
modulation corresponding to the specific phase can be applied to
reconstructing illumination light by the thus constructed physical
cell. Even if a convex part, instead of the concave part, is formed
on the block-like physical cell, similar modulation processing can
be applied. That is, even if the dimension G2 is set at a negative
value, and a projection instead of the groove is formed on the
physical block shown in FIG. 8, it is possible to produce an
optical path difference corresponding to the height of the
projection and produce a phase difference. In other words, if a
part having an area corresponding to the specific amplitude of the
upper surface of the block-like physical cell is protruded by the
height corresponding to the specific phase so as to form a convex
part, the amplitude modulation corresponding to the specific
amplitude and the phase modulation corresponding to the specific
phase can also be applied to reconstructing illumination light by
the thus constructed physical cell.
[0113] The width G1 and depth G2 of the groove can be consecutively
changed in the physical cell C(x, y) having the groove G(x, y)
shown in FIG. 8, and therefore, theoretically, infinite kinds of
physical cells can be prepared. The use of the infinite kinds of
physical cells makes it possible to replace the virtual cell with
the physical cell having the accurate groove width G1 corresponding
to the specific amplitude and the accurate depth G2 corresponding
to the specific phase that are defined in the virtual cell.
However, practically, it is preferable to predetermine .alpha.
kinds of groove widths and .beta. kinds of depths so as to prepare
.alpha..times..beta. kinds of physical cells in total and then
select a physical cell closest in necessary optical properties from
among the physical cells. FIG. 11 is a perspective view showing an
example in which seven kinds of groove widths and four kinds of
depths are determined so as to prepare 28 kinds of physical cells
in total. Each of the 28 kinds of physical cells is a block-like
physical cell formed as shown in FIG. 8, and, in FIG. 11, the
physical cells are arranged in the form of a matrix of four rows
and 7 columns.
[0114] In FIG. 11, the seven columns of the matrix indicate the
variation of amplitude A, and the four rows thereof indicate the
variation of phase .theta.. For example, the cell located at column
W1 is a cell corresponding to the minimum value of amplitude A,
wherein groove width G1=0, i.e., a groove G is not formed at all.
Rightward, i.e., toward columns W2 to W7, the cells correspond to
greater amplitude A, and the groove width G1 thereof gradually
becomes greater. The cell located at column W7 is a cell
corresponding to the maximum value of amplitude A, wherein groove
width G1=cell width C1, i.e., the entire surface thereof is
hollowed. Further, when attention is paid to the rows of the matrix
of FIG. 11, the cell located at row V1, for example, is a cell
corresponding to the minimum value of phase .theta., wherein groove
depth G2=0, i.e., a groove G is not formed at all. Downward, i.e.,
toward rows V2 to V4, the cells correspond to greater phase
.theta., and the groove depth G2 thereof gradually becomes
greater.
[0115] .sctn. 4. Optical Element Manufacturing Method by Use of
Practical Physical Cells
[0116] Now, a description will be provided of a concrete method for
manufacturing an optical element (hologram-recording medium) where
an object image 10 is recorded by use of 28 kinds of physical cells
shown in FIG. 11. First, as shown in FIG. 5, the object image 10
formed by a set of point light sources and a three-dimensional
virtual cell set 30 are defined by use of a computer. Herein,
respective virtual cells that make up the three-dimensional virtual
cell set 30 are block-like cells (at this moment, a groove has not
yet been formed) as shown in FIG. 8, and the three-dimensional
virtual cell set 30 is formed by arranging the cells
two-dimensionally and with equal pitches vertically and
horizontally. The dimension of one virtual cell should be, for
example, C1=0.6 .mu.m, C2=0.25 .mu.m, and C3=0.25 .mu.m or so. In
this case, if the lateral pitch of the cell is 0.6 .mu.m, and the
longitudinal pitch is 0.25 .mu.m, the cells can be disposed without
any gap. Of course, the dimensional value of each cell shown here
is one example, and, in practice, it is possible to set it at an
arbitrary dimension if necessary. However, as the cell dimension
becomes greater, the visual angle by which a reconstructed image of
an object is obtained is narrowed, and the resolution of the object
is lowered proportionately. Reversely, as the cell dimension
becomes smaller, the processing of forming a concave/convex
structure of the physical cell technically becomes difficult. In
consideration of the arithmetic processing or the convenience of
the processing of the physical cells, it is preferable to dispose
the cells with predetermined equal pitches vertically and
horizontally though they do not necessarily need to be disposed
with equal pitches.
[0117] After the definition of the object image 10 and the
definition of the three-dimensional virtual cell set 30 are
completed, a representative point is defined in each virtual cell,
and then the complex amplitude of the composite wave of each object
light that has reached each representative point is calculated as
described in .sctn. 2, and a specific amplitude and a specific
phase are defined for each virtual cell. Thereafter, each virtual
cell is replaced with any one of the 28 kinds of physical cells
shown in FIG. 11 (in other words, it is replaced with a physical
cell closest in optical properties needed for modulation according
to the specific amplitude and the specific phase defined in each
individual virtual cell), and an optical element is formed as a set
of physical cells. At this time, the groove-forming surface of each
physical cell (in the case of the physical cell shown in FIG. 8 or
FIG. 11, the upper surface) is designed to face the front surface
(i.e., the surface facing the object image 10) of the
three-dimensional virtual cell set 30 shown in FIG. 5.
[0118] In fact, the replacement of the virtual cell with the
physical cell is carried out as the processing of forming a given
concave/convex structure on the surface of a medium to become an
optical element. Since the physical cell is disposed so that its
groove is directed forward when each virtual cell of the
three-dimensional virtual cell set 30 shown in FIG. 5 is replaced
with the physical cell as mentioned above, a finally formed optical
element appears as a medium whose surface has a concave/convex
structure formed with many grooves. Therefore, the replacement of
the virtual cell with the physical cell is carried out as
processing of providing data relative to a concave/convex pattern
to a drawing device from a computer that stores information for
each virtual cell (i.e., information that shows the specific
amplitude and the specific phase defined in each virtual cell) and
then drawing the concave/convex pattern onto the physical surface
of the medium by the drawing device. The processing of drawing a
fine concave/convex pattern can be carried out by, for example, a
patterning technique that uses an electron-beam drawing device.
What is needed to mass-produce the same optical element is to form
an original plate in which a desired concave/convex structure is
formed by the drawing processing that uses an electron-beam drawing
device, for example, and to transfer the concave/convex structure
onto many mediums by the stamping step that uses the original
plate.
[0119] The optical element according to the present invention is
basically formed with a main body layer that is obtained by
two-dimensionally arranging the physical cells shown in FIG. 8.
However, a protective layer may be placed on the surface of the
main body layer if necessary. This protective layer serves to cover
the concave/convex surface formed in the surface of the main body
layer. The main body layer and the protective layer are made of
materials different from each other.
[0120] In a transmission type optical element in which incidence
light given to each physical cell passes through the main body
layer and the protective layer and then turns into emission light,
the main body layer and the protective layer must be made of a
transparent material and another transparent material,
respectively, that are different in the refractive index. Here, let
us consider a concrete relationship between the depth of the groove
G and the phase when a transmission type optical element (i.e.,
transmission type physical cell) of a two-layer structure made of
such a main body layer and a protective layer is manufactured.
[0121] Now, let us consider a transmission type cell C(x, y) having
a structure shown in the sectional view of the upside of FIG. 12.
This is a cell having a two-layer structure made of a main body
layer Ca in which a groove G whose depth is d(x, y) is formed and a
protective layer Cb placed on the upper surface thereof in such a
way as to fill the groove G. Herein, the refractive index of a
material that forms the protective layer Cb (in other words, the
refractive index of a material with which the concave part is
filled or a material that constitutes the convex part) is
represented as n1, and the refractive index of a material that
forms the main body layer Ca is represented as n2. If the maximum
depth dmax of the groove G (in other words, the maximum depth of
the concave part or the maximum height of the convex part) is set
to be dmax=.lambda./.vertline.n1-n2.vertline., a physical cell can
be realized in which phase modulation within the range of 0 through
2 .pi. can be applied to light whose wavelength is .lambda.. For
example, if the wavelength .lambda. equals 400 nm (.lambda.=400 nm)
and the difference .vertline.n1-n2.vertline. in the refractive
index equals 2, the maximum depth can be set to be dmax=200 nm (0.2
.mu.m).
[0122] In this case, as shown in FIG. 12, the depth d(x, y)
corresponding to the specific phase .theta.(x, y) can be obtained
by the following equations:
[0123] If n1>n2,
d(x, y)=.lambda..multidot..theta.(x, y)/2(n1-n2).pi.
[0124] and, if n1<n2,
d(x, y)=dmax-.lambda..multidot..theta.(x, y)/2(n2-n1).pi.
[0125] Accordingly, after the specific amplitude and specific phase
of a certain virtual cell C(x, y) are obtained as A(x, y) and
.theta.(x, y), respectively, the specific phase .theta.(x, y) is
substituted for the above equation so as to calculate a
corresponding depth d(x, y), and then a physical cell that has a
depth closest to the resulting depth d(x, y) and has a width
closest to the dimension corresponding to the specific amplitude
A(x, y) is selected from among the 28 kinds of physical cells shown
in FIG. 11, and the replacement of the virtual cell C(x, y) with
the selected physical cell is carried out. If the protective layer
Cb is not provided, the refractive index of air (almost 1) can be
used as the refractive index n1 of the protective layer.
[0126] On the other hand, let us consider a reflection type cell
C(x, y) having a structure shown in the sectional view of the
upside of FIG. 13. This is a cell having a two-layer structure made
of a main body layer C .alpha. in which a groove G whose depth is
d(x, y) is formed and a protective layer C .beta. placed on the
upper surface thereof in such a way as to fill the groove G. In
this cell, the boundary between the main body layer C .alpha. and
the protective layer C .beta. serves as a reflecting surface. The
reflectance on this reflecting surface is not necessarily to be
100%. The reflecting surface may be a half-mirror having a
reflectance of e.g. 50%. The reflecting surface is also provided by
inserting a half transparent layer such as a transflector between
the main body layer C .alpha. and the protective layer C .beta..
Incidence light that has struck the protective layer C .beta. from
the upper side of the figure downward is reflected by the
reflecting surface and is emitted upward in the figure. Herein, the
refractive index of a material that forms the protective layer C
.beta. (in other words, the refractive index of a material with
which the concave part is filled or a material that constitutes the
convex part) is represented as n. If the maximum depth dmax of the
groove G (in other words, the maximum depth of the concave part or
the maximum height of the convex part) is set to be
dmax=.lambda./2n, a physical cell can be realized in which phase
modulation within the range of 0 through 2 .pi. can be applied to
light whose wavelength is .lambda.. For example, if the wavelength
.lambda. equals 400 nm (.lambda.=400 nm) and the refractive index
equals 2 (n=2), the maximum depth can be set to be dmax=100 nm (0.1
.mu.m).
[0127] In this case, as shown in FIG. 13, the depth d(x, y)
corresponding to the specific phase .theta.(x, y) is obtained by
the following equation:
d(x, y)=.lambda..multidot..theta.(x, y)/4n .pi.
[0128] If the protective layer C .beta. is not provided, the
refractive index of air (almost 1) can be used as the refractive
index n of the protective layer. Accordingly, the maximum depth of
the groove G can be set to be dmax=.lambda./2, and the depth d(x,
y) corresponding to the specific phase .theta.(x, y) can be
determined by the following equation:
d(x, y)=.lambda..multidot..theta.(x, y)/4 .pi.
[0129] .sctn. 5. Modification in Consideration of Convenience of
Reconstructive Environment
[0130] Let us now consider an environment in which reconstructing
illumination light is projected onto the optical element
manufactured according to the method described above so as to
reconstruct the object image 10 recorded as a hologram. FIG. 14 is
a side view showing the relationship among an optical element 40
(i.e., hologram-recording medium that uses physical cells),
reconstructing illumination light Lt or Lr, and a viewing point E
that are used for the reconstruction. If the optical element 40 is
a transmission type element that uses transmission type cells, the
reconstructing illumination light Lt is projected to the surface
opposite to the viewing point E as shown in the figure, and light
that has passed through the optical element 40 is observed at the
viewing point E. If the optical element 40 is a reflection type
element that uses reflection type cells, the reconstructing
illumination light Lr is projected to the surface on the same side
as the viewing point E as shown in the figure, and light that has
been reflected from the optical element 40 is observed at the
viewing point E. In any case, when the optical element 40 is
manufactured according to the above method, the most excellent
reconstructed image can be obtained in the condition that the
reconstructing illumination light Lt or Lr is given as a plane wave
of monochromatic light and projected in the normal direction to the
recording surface (i.e., a two-dimensional array surface on which
physical cells are arranged) of the optical element 40 as shown in
FIG. 14 (in other words, reconstructing illumination light is
projected so that the wave front becomes parallel with the
recording surface of the optical element 40), and the image is
observed in the normal direction to the recording surface.
[0131] However, the actual reconstructive environment of the
optical element 40 where the object image 10 is recorded as a
hologram does not necessarily lead to the ideal environment shown
in FIG. 14. Especially, in the case of the reflection type, since a
head of an observing person is located at the position of the
viewing point E, a shadow of the person, which makes the excellent
reconstruction impossible, appears on the optical element 40 even
if the reconstructing illumination light Lr is projected from the
direction shown in FIG. 14. Therefore, generally, the actual
reconstructive environment has an aspect in which the
reconstructing illumination light Lt or Lr is projected in the
oblique direction with respect to the recording surface of the
optical element 40 so as to observe the reconstructed image at the
viewing point E located in the normal direction as shown in FIG.
15, or, alternatively, an aspect in which the reconstructing
illumination light Lt or Lr is projected in the normal direction to
the recording surface of the optical element 40 so as to observe
the reconstructed image at the viewing point E located in the
oblique direction as shown in FIG. 16, or, alternatively, an aspect
in which both the projecting direction of the reconstructing
illumination light Lt or Lr and the observing direction with
respect to the viewing point B are set as the oblique
direction.
[0132] What is needed to manufacture the optical element 40 by
which an excellent reconstructed image can be obtained in the
actual reconstructive environment is to carry out phase-correcting
processing in which the specific phase defined for each virtual
cell is corrected, in consideration of the direction of the
illumination light projected when reconstructed and the position of
the viewing point when reconstructed.
[0133] For example, let us consider a case in which, as shown in
FIG. 17, reconstructing illumination light rays L1 through L4 are
projected in the oblique direction, and light rays LL1 through LL4
that have undergone modulation of the amplitude and the phase as a
result of passing through the optical element 40 (in other words,
light rays LL1 through LL4 have the reconstructed wave front of the
object light emitted from the object image 10) are observed at the
viewing point E located in the normal direction. If the
reconstructing illumination light rays L1 through L4 are each a
monochrome plane wave whose wavelength is A and if the
reconstructing illumination light is projected onto the optical
element 40 in the oblique direction, an optical path difference
will have already arisen when the light reaches each point P1
through P4 on the optical element 40, and incidence light at each
point P1 through P4 will have already generated a phase difference.
For example, the incidence light rays upon the positions of points
P2, P3, and P4 are longer in the optical path length by d2, d3, and
d4, respectively, than the incidence light ray upon the position of
point P1. Therefore, the incidence light has already generated a
phase difference in proportion to the optical path difference.
Therefore, if there is the supposition that "the optical element 40
is manufactured by which an excellent reconstructed image can be
obtained in the reconstructive environment shown in FIG. 17", the
specific phase about each virtual cell can be calculated according
to the above-mentioned method, and thereafter the processing of
correcting each specific phase can be carried out in accordance
with the position of the cell. For example, there is no need to
correct the cell located at the position of point P1 of FIG. 17,
and the cell located at the position of point P2 undergoes the
correction of the specific phase so as to cancel a phase difference
caused by the optical path difference d2. Accordingly, if the
optical element 40 is manufactured while carrying out the
correction of the specific phase, an excellent reconstructed image
can be given by the light rays LL1 through LL4 emitted toward the
viewing point E.
[0134] This corrective processing to the specific phase is likewise
carried out in a case in which, as shown in FIG. 18, the
reconstructing illumination light rays L1 through L4 are projected
in the normal direction so as to observe the light rays LL1 through
LL4 that have undergone modulation of the amplitude and the phase
as a result of passing through the optical element 40 (i.e., light
that has reconstructed the wave front of the object light from the
object image 10) at the viewing point E located in the oblique
direction. That is, if the reconstructing illumination light rays
L1 through L4 are each a monochrome plane wave whose wavelength is
.lambda. and if the reconstructing illumination light rays are
projected onto the optical element 40 in the normal direction, no
optical path difference occurs when the light ray reaches each
point P1 through P4 on the optical element 40, and the phases of
the incidence light rays upon points P1 through P4 coincide with
each other. However, a difference arises among the optical path
lengths from points P1 through P4 to the viewing point E that the
emission light emitted therefrom reaches, and a phase difference
will arise when observed at the viewing point E. For example, the
emission light rays from the positions of points P2, P3, and P4 are
longer in the optical path length by d2, d3, and d4, respectively,
than the emission light ray from the position of point P1.
Therefore, the emission light has generated a phase difference in
proportion to the optical path difference at the position of the
viewing point E. Therefore, if there is the supposition that "the
optical element 40 is manufactured by which an excellent
reconstructed image can be obtained in the reconstructive
environment shown in FIG. 18", the specific phase about each
virtual cell can be calculated according to the above-mentioned
method, and thereafter the processing of correcting each specific
phase can be carried out in accordance with the position of the
cell. For example, there is no need to correct the cell located at
the position of point P1 of FIG. 18, and the cell located at the
position of point P2 undergoes the correction of the specific phase
so as to cancel a phase difference caused by the optical path
difference d2. Accordingly, if the optical element 40 is
manufactured while carrying out the correction of the specific
phase, an excellent reconstructed image can be provided by the
light rays LL1 through LL4 emitted toward the viewing point E.
[0135] The corrective processing to the specific phase for the
transmission type optical element 40 was described above. The same
principle of the corrective processing applies to the reflection
type optical element 40.
[0136] On the other hand, concerning the wavelength of the
reconstructing illumination light, a case where monochromatic light
whose wavelength is .lambda. can be used as reconstructing
illumination light is extremely rare in the actual reconstructive
environment, and therefore, normally, a case where the
reconstruction is carried out under reconstructing illumination
light close to white can be regarded as general. If the
reconstruction is carried out by use of reconstructing illumination
light that includes a plurality of wavelength components, different
phase modulation is performed for light having each individual
wavelength, and therefore an excellent reconstructed image cannot
be obtained. Concretely, a reconstructed image is formed as if
images with various colors are superimposed on each other with
slight incongruity.
[0137] Therefore, in order to obtain a fairly excellent
reconstructed image even in the reconstructive environment that
uses white reconstructing illumination light, a method, such as
that shown in FIG. 19, should be applied when a complex amplitude
distribution of object light is calculated. Like the system shown
in FIG. 5, a system shown in FIG. 19 is used to define the object
image 10 and the three-dimensional virtual cell set 30 on a
computer and calculate for obtaining a distribution of the totaled
complex amplitude of each object light emitted from the object
image 10 on the three-dimensional virtual cell set 30. Herein, the
three-dimensional virtual cell set 30 is constructed by arranging
virtual cells horizontally and vertically, and is a cell set that
consists of the virtual cells arranged on the two-dimensional
matrix. Representative points are defined in the virtual cells,
respectively.
[0138] When the technique described herein is employed, the totaled
complex amplitude at the position of each representative point is
calculated by the following method. First, a plurality of M
point-light-source rows each of which extends horizontally and
which are mutually arranged vertically are defined on the object
image 10. In the example of the figure, M=3, and three point light
source rows m1, m2, and m3 are defined. Each point light source row
includes a plurality of point light sources arranged horizontally.
For example, a point light source row m1 includes j point light
sources O(m1,1), O(m1,2), . . . , O(m1,j). On the other hand, on
the side of the three-dimensional virtual cell set 30, M groups in
total are defined by defining groups of virtual cells that belong
to a plurality of rows contiguous vertically as one group in the
two-dimensional matrix. In the example of the figure, three groups
in total are defined as M=3. That is, a first group g1 consists of
virtual cells that belong to first through third rows, a second
group g2 consists of virtual cells that belong to fourth through
sixth rows, and a third group g3 consists of virtual cells that
belong to seventh through ninth rows.
[0139] The M point light source rows are thus defined on the side
of the object image 10, and the M groups are defined on the side of
the three-dimensional virtual cell set 30. Thereafter, the M point
light source rows and the M groups are caused to correspond to each
other in accordance with the arrangement order concerning the
vertical direction. That is, in the example of the figure, the
uppermost point light source row m1 is caused to correspond to the
uppermost group g1, the middle point light source row m2 is caused
to correspond to the middle group g2, and the lowermost point light
source row m3 is caused to correspond to the lowermost group g3.
Thereafter, on the supposition that the object light emitted from a
point light source in the m-th point light source row (m=1 to M)
reaches only the virtual cell that belongs to the m-th group, the
totaled complex amplitude at the position of each representative
point is calculated. For example, the object light emitted from the
point light sources O(m1,1), O(m1,2), . . . , O(m1,j) that belong
to the point light source row m1 in FIG. 19 is regarded as reaching
only the virtual cells that belongs to the group g1 (virtual cells
arranged in the first to third rows), and as not reaching the
virtual cells that belongs to the groups g2 and g3, and the totaled
complex amplitude is calculated. In other words, the calculation of
the totaled complex amplitude at the position of the representative
point of the virtual cell that belongs to the group g1 is carried
out in consideration of only the object light emitted from the
point light sources O(m1,1), O(m1,2), . . . , O(m1,j) that belong
to the point light source row m1, not in consideration of the
object light emitted from the point light sources that belong to
the point light source rows m2 and m3.
[0140] Actually, the object image 10 cannot be recorded as an
original hologram if it is recorded under these conditions. After
all, the basic principle of the hologram resides in that all
information for the object image 10 is recorded onto any places of
the recording surface, and thereby a stereoscopic image can be
reconstructed. If the object image 10 is recorded under the
conditions mentioned above, only information of a part of the
point-light-source row m1 (i.e., part of the upper portion of the
object image 10) is recorded in the area of the group g1. As a
result, a stereoscopic reconstructed image as an original hologram
cannot be obtained. Concretely, stereoscopic vision relative to the
horizontal direction can be given, but stereoscopic vision relative
to the vertical direction becomes insufficient. However, if the
object image 10 is recorded under these conditions, a more
excellent reconstructed image (i.e., an even clearer reconstructed
image including the fact that the stereoscopic vision relative to
the vertical direction is insufficient) can be obtained in the
reconstructive environment that uses white reconstructing
illumination light. The reason is that,when reconstructed, an
effect to control the wavelength distribution of the reconstructing
light concerning with the vertical direction can be obtained by
recording the object image 10 in such a way as to divide it into
parts concerning with the vertical direction.
[0141] The present invention was described on the basis of the
embodiments shown in the figures. However, the present invention is
not limited to these embodiments, and can be carried out in various
forms. For example, in the above embodiment, the three-dimensional
virtual cell set 30 is defined by arranging three-dimensional cells
like a two-dimensional matrix. However, it is also possible to
define the three-dimensional virtual cell set 30 by preparing
three-dimensional cells that are slender in the horizontal
direction as shown in FIG. 20 and arranging the three-dimensional
cells like a one-dimensional matrix. In the example of FIG. 20,
cells C(1), C(2), C(3), . . . , which are slender in the horizontal
direction, are arranged in the vertical direction so as to form the
three-dimensional virtual cell set 30. If the object image 10 is
recorded onto an optical element that consists of cells arranged
like a one-dimensional matrix in this way, only the reconstructed
image in which only the stereoscopic vision relative to the
vertical direction can be given will be obtained, but this is
satisfactorily useful depending on its usage.
[0142] The optical element according to the present invention, of
course, can be used as a "hologram-recording medium" in which some
object image 10 is recorded as a hologram, and then is
reconstructed as a stereoscopic image. However, the present
invention is not limited to usage as the hologram-recording medium,
and can also be applied to a case in which a general optical
element, such as an optical filter, a polarized light element, or a
light modulating element, is manufactured. For example, if a
pattern of a simple lattice design is used as the object image 10,
and a complex amplitude distribution of object light emitted from
this pattern is recorded onto a physical medium, an optical element
with peculiar optical properties can be realized.
[0143] Further, the three-dimensional cells are not necessarily
needed to be arranged along a rectangular coordinate system. For
example, they can also be arranged along a spherical surface by use
of a polar coordinate system. Additionally, the three-dimensional
physical cells used in the above embodiments are cells serving as
passive elements. However, the physical cells used in the present
invention may be constructed by active elements capable of
controlling the refractive index, transmittance, reflectivity,
etc., on the basis of a signal from the outside. For example, if
each individual physical cell is made of a birefringent material
like a liquid crystal, and the ratio of an ordinary ray to an
extraordinary ray is controlled according to an outside signal, the
specific amplitude and specific phase of the physical cell can be
determined on the basis of a signal given from the outside. In the
optical element that uses the active element as a physical cell,
since a recorded image is not physically fixed, an arbitrary object
image can be reconstructed in accordance with a signal from the
outside.
[0144] As described above, according to the present invention, high
diffraction efficiency can be obtained when reconstructed since an
object image is recorded as a complex amplitude distribution of
object light, not as interference fringes. Moreover, since the
complex amplitude distribution is recorded while employing the
optical properties of a three-dimensional cell, an optical element
superior in productivity can be provided.
* * * * *